A method for predicting silicon concentration in rivers under different runoff conditions

Abstract

The present invention belongs to the technical field of river solute concentration prediction and provides a new method for predicting river silicon concentration under different runoff conditions. By using long-term series river runoff depth data and river silicon concentration data at high and low runoff depths, the baseflow index (BFI) and fitting parameters α, n, A, and B are obtained to construct a silicon concentration prediction model to estimate river silicon concentration under different runoff conditions. By introducing the baseflow index, the present invention proposes a new approach to predicting river silicon concentration, namely, scaling and translating the baseflow index-runoff depth relationship to construct a silicon concentration prediction model, thereby predicting river silicon concentration under different runoff conditions. The model fitting values ​​of this method have a good match with the observed values; it only requires measuring the river runoff depth and the concentration at low and high runoff depths, and the model data and parameters are relatively easy to obtain.

Description

Technical Field

[0001] The invention belongs to the technical field of river solute concentration prediction, and in particular relates to a method for predicting silicon concentration in rivers at different runoff depths. Background Art

[0002] Rivers are a crucial link in the surface water cycle. In the global silicon cycle, most of the silicon input into the world's oceans comes from river transport. Silicon is currently one of the key elements of focus in global environmental change research.

[0003] There are various methods for predicting river silicon concentrations, such as the mixing model of Johnson et al. (1969) and the chemical model of Langbein and Dawdy (1964). The Langbein and Dawdy (1964) chemical model assumes that water reacts rapidly with soil and rock, and can ignore the mixing of water of different compositions or concentrations. However, its specific conditions are difficult to meet. The mixing model derived by Johnson et al. (1969) is based on the mixing of water of different concentrations, and the required parameters are difficult to obtain. Its formula is as follows:

[0004]

[0005] Where: a is the concentration of the solute in low-concentration water, often considered to be the concentration in rainfall, μmol / L; b is the average residence time / V Q＝0 (V Q＝0 represents the water storage capacity of the basin when the discharge flow at the basin outlet is 0), s / m 3 ; d is the solute concentration difference between high and low concentration water, μmol / L; Q is the flow rate, m 3 / s. Summary of the Invention

[0006] The present invention derives a new model for the change of river silicon concentration with river runoff through the relationship between river runoff depth, base flow index BFI and river silicon concentration, which is used to predict river silicon concentration under different river runoffs.

[0007] The present invention is achieved by a method for predicting the silicon concentration in a river by the depth of river runoff, such as Figure 1 The following steps are shown:

[0008] Step 1: Obtain long-term series river runoff depth data h.

[0009] Step 2: Calculate the baseflow index BFI based on the long-term runoff depth data h, and obtain the fitting parameters α and n.

[0010] Step 3: Obtain the concentration data of the river at low and high runoff depths to obtain the fitting parameters A and B.

[0011] Step 4: Based on the above model parameters, a prediction model is constructed to predict the silicon concentration in the river.

[0012] Furthermore, in step one, long-term series runoff depth data of the river is obtained.

[0013] Furthermore, in step 2, the BFI is calculated based on the runoff depth data using the local-min method (Beck et al., 2015).

[0014] The base flow index BFI and runoff depth h have the following empirical relationship:

[0015] BFI=α·h n (2)

[0016] Where: h is the river runoff depth, mm / month; α is the fitting parameter; n is the fitting parameter.

[0017] With runoff depth h as the x-axis and baseflow index (BFI) as the y-axis, a power relationship graph was plotted between baseflow index (BFI) and runoff depth h. The maximum and minimum BFI values, as well as the fitting parameters α and n, were determined based on the trend line.

[0018] Furthermore, in step 3, the maximum and minimum silicon concentrations in the river can be obtained by arithmetic averaging the concentration data at low and high runoff depths. To predict the silicon concentration in the river, the maximum and minimum BFI values, the maximum and minimum silicon concentrations in the river, and the fitting parameters α and n are substituted into the following formula:

[0019]

[0020] Where: C is the predicted river silicon concentration, μmol / L; C max is the maximum silicon concentration in the river, μmol / L; C min is the minimum silicon concentration in the river, μmol / L; BFI max is the maximum value of base flow index; BFI min is the minimum value of the baseflow index.

[0021] make For A, let If B is used, formula (3) can be simplified to obtain formula (4):

[0022] C=A·α·h n +B (4)

[0023] Furthermore, in step 4, the silicon concentration in the river is estimated using the model parameters estimated in steps 1 to 3 and formula (4).

[0024] In summary, the advantages and positive effects of the present invention are:

[0025] Introducing the baseflow index, a new approach to predicting river silicon concentrations has been proposed. This involves scaling and translating the baseflow index-runoff relationship to construct a silicon concentration prediction model, which can then predict river silicon concentrations under varying runoff conditions. The model fits well with observed values. This method only requires measuring river runoff depth, and concentrations at low and high runoff depths, making the model data and parameters readily available. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 Schematic diagram of the method for predicting silicon concentration at different runoff depths in rivers;

[0027] Figure 2 This is the BFI-h power relationship diagram for McDonalds River in the United States;

[0028] Figure 3 A comparison chart of predicted and observed silicon concentrations in McDonalds River, USA; DETAILED DESCRIPTION

[0029] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present method is further described in detail below with reference to examples.

[0030] The present invention provides a method for predicting silicon concentration in a river, comprising the following steps:

[0031] Step 1: Obtain river runoff depth data h for at least ten years.

[0032] Step 2: Calculate the base flow index BFI based on the runoff depth data h, and obtain the fitting parameters α and n.

[0033] Step three: obtain the concentration data of the river at low and high runoff depths, that is, the concentration data corresponding to the first 10% and the concentration data corresponding to the last 10% of the runoff depth data arranged from small to large, so as to obtain the fitting parameters A and B.

[0034] Step 4: Based on the above model parameters, a prediction model is constructed to predict the silicon concentration in the river.

[0035] In the step 1, the runoff depth data h of the McDonalds River for the past 50 years is obtained from the Hydrological Benchmark Network (HBN) of the United States Geological Survey (USGS).

[0036] In step 2, the baseflow index (BFI) was calculated based on the runoff depth data using the USGS GW Toolbox 1.3.1 (Barlow et al., 2017) software using the local-min method (Beck et al., 2015).

[0037] With runoff depth h as the x-axis and base flow index BFI as the y-axis, a power relationship diagram of base flow index BFI and runoff depth h is drawn. According to the empirical relationship (2) and the trend line relationship, the maximum base flow index BFI of McDonalds River in the United States is obtained. max The minimum base flow index is 1.0. min is 0.8, the fitting parameter α is 1.3765, and n is -0.132. Figure 2 shown.

[0038] In step 3, the concentration data corresponding to the low and high runoff depths of McDonalds River were obtained from the Hydrological Benchmark Network (HBN) of the United States Geological Survey (USGS), and the maximum silicon concentration C of McDonalds River was obtained by arithmetic averaging. max The minimum silicon concentration is 87 μmol / L. min It is 40μmol / L.

[0039] The maximum value of the base flow index BFI max , minimum base flow index BFI min , the maximum silicon concentration in the river C max , minimum silicon concentration in rivers C min Substitution and Calculation shows that A is 235 and B is -148.

[0040] Furthermore, in step 4, the silicon concentration in the river is estimated using the model parameters estimated in steps 1 to 3 and formula (4).

[0041] Using data from the McDonalds River Basin in the United States, the results of the hybrid model of Johnson et al. (1969) were compared with the results of this model. The residual RMSE between the simulated values ​​and the observed values ​​derived by the hybrid model of Johnson et al. (1969) was 11.6, while the RMSE of this model was 12.1, indicating that the results of the two models are approximately comparable. Figure 3 shown.

[0042] References:

[0043] Barlow,P.,Cunningham,W.,Zhai,T.and Gray,M.(2017)US Geological SurveyGroundwater Toolbox version 1.3.1,a graphical and mapping interface foranalysis of hydrologic data:US Geological Survey Software Release,26May 2017.

[0044] Beck,H.E.,De Roo,A.and van Dijk,A.I.(2015)Global maps of streamflowcharacteristics based on observations from several thousandcatchments.Journal of Hydrometeorology 16,1478-1501.

[0045] Johnson,N.M.,Likens,G.E.,Bormann,F.H.,Fisher,D.and Pierce,R.S.(1969)Aworking model for the variation in stream water chemistry at the HubbardBrook Experimental Forest,New Hampshire.Water Resources Research 5,1353-1363.

[0046] Langbein,W.and Dawdy,D.(1964)Occurrence of dissolved solids insurface waters in the United States.USGS Professional Paper 501-D,115-117.

Claims

1. A method for predicting silicon concentration in rivers under different runoff conditions, characterized in that Follow the steps below: Step 1: Obtain long-term series river runoff depth data; Step 2: Calculate the baseflow index (BFI) based on the long-term runoff depth data and obtain the fitting parameters α and n; Step 3: Obtain the concentration data of the river at low and high runoff depths to obtain the fitting parameters A and B; Step 4: Based on the above fitting parameters, construct the silicon concentration prediction model C = A·α·h n +B and predict river silicon concentrations; In step 2, the BFI is calculated using the local-min method based on the runoff depth data; with the runoff depth as the x-axis and the base flow index BFI as the y-axis, an empirical relationship diagram of the base flow index BFI and the runoff depth h power is drawn, and the maximum BFI value BFI is determined according to the trend line. max and minimum BFI min , and the empirical relationship BFI = α·h n The fitting parameters α and n; Among them, in step 3, based on the silicon concentration data of the river at low and high runoff depths, the maximum silicon concentration C of the river can be obtained by arithmetic averaging. max and the minimum silicon concentration C min , together with the maximum BFI BFI max and minimum BFI min Substitution and Calculate and obtain the fitting parameters A and B.

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